Reply by pete79

I just did something like this a couple days ago….drill a pilot hole all the way through the piece with a smaller bit than the hole saw’s (first pic) pilot bit uses. Then use the hole saw to cut part way through the piece, flip the piece over and cut with hole saw from other side. If the hole saw is less than 1.5” deep, you should be able to just grab the waste and pull it out. If not, there should be a hole in the back of it to let you punch it out of the saw.

This is the same method that is typically used for cutting holes in doors for door handles and seems to work pretty well.